Generalized threshold decoding of linear codes

It is proved that every linear code of dimension
k
can be decoded by a threshold decoding circuit that is guaranteed to correct
e
errors if
e \leq (d - 1)/2
where
d
is the minimum distance of the code. Moreover it is demonstrated that the number of levels of threshold logic is less than or equal to
k
by giving an algorithm for generating the decoding logic employing
k
levels.